Answer in written paper

Consider the following definitions. Definition. An integer n is alphic if n = 4k + 1 for some integer k. Definition. An integer n is gammic if n = 4k + 3 for some integer k. a) Show that 19 is gammic. b) Suppose that a is alphic and y is gammic. Prove that a + y is even. c) Prove by contraposition: If r is not odd, then r is not alphic